Question

As shown in the figure, two large black plane surfaces are maintained at constant temperature $T_1$ and $T_2(T_1>$ $T_2$ ). Two thin black plates are placed between the two surfaces and in parallel to them. After some time, steady conditions are obtained. The ratio of heat transfer rate between plate- $1$ and plate- $3$ to the ratio of original (when plate-$3$ and plate-$4$ was not present) heat tranfer rate between plate-$1$ and plate-$2$ in steady state is $\eta$. Find $\frac{1}{\eta }$.

Answer 1

Answer: 3

$Q=\sigma \left(T_1^4-T_3^4\right)W/m^2$
$=\sigma \left(T_3^4-T_4^4\right)W/m^2$
$=\sigma \left(T_4^4-T_2^4\right)W/m^2$
$3Q=\sigma \left(T_1^4-T_2^4\right)=Q_{0}W/m^2$
$\eta =\frac{Q}{Q_0}=\frac{1}{3}$